Stability analysis of fractional-order Colpitts oscillators


The mathematical formulae of six topologies of fractional-order Colpitts oscillator are introduced in this paper. Half of these topologies are based on MOS transistor, and the other half is based on BJT transistor. The design procedure for all of these topologies is proposed and summarized for each one. Stability analysis is very crucial in oscillators’ design, as oscillators should have its poles on the imaginary axis to obtain a sustained oscillation. Hence, determining the factors that control the oscillator’s stability is very important. An intensive study of the stability of Colpitts oscillator is introduced, including different cases for all topologies. Additionally, circuit simulation is conducted using Valsa’s emulator of the fractional-order capacitor for validating the mathematical formulae and the stability criteria. Experimental work is also included to verify the mathematical findings and circuit simulations. © 2019, Springer Science+Business Media, LLC, part of Springer Nature.


Said L.A., Elwy O., Madian A.H., Radwan A.G., Soliman A.M.


Colpitts; Fractional-order capacitor; Fractional-order circuits; Oscillators; Stability; Valsa’s network

Document Type



Analog Integrated Circuits and Signal Processing, Vol. 101, PP. 267 to 279, Doi: 10.1007/s10470-019-01501-2

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